Standing waves for quasilinear Schrödinger equations involving double exponential growth

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Abstract

We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.

Original languageEnglish
Pages (from-to)1682-1695
Number of pages14
JournalAIMS Mathematics
Volume8
Issue number1
DOIs
StatePublished - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2023, American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Trudinger-Moser inequality
  • double exponential growth
  • dual approach
  • mountain pass theorem
  • quasilinear Schrödinger equation

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